Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #1141 : Plane Geometry

A right isosceles triangle is stacked on top of a square as shown in the figure. Find the perimeter of the compound shape.

7

Possible Answers:

Correct answer:

Explanation:

13

Notice that the hypotenuse of the right isosceles triangle is also the length of a side of the square.

First, we will need to find the length of the legs of the triangle by using the Pythagorean theorem.

Substitute in the given length of the hypotenuse to find the length of the leg of the triangle.

13

In order to find the perimeter, add up the lengths outlined in red. The perimeter includes the two legs of the triangle and three sides of the square.

Therefore:

Example Question #1142 : Basic Geometry

A right isosceles triangle is stacked on top of a square as shown in the figure. Find the perimeter of the compound shape.

8

Possible Answers:

Correct answer:

Explanation:

13

Notice that the hypotenuse of the right isosceles triangle is also the length of a side of the square.

First, we will need to find the length of the legs of the triangle by using the Pythagorean theorem.

Substitute in the given length of the hypotenuse to find the length of the leg of the triangle.

13

In order to find the perimeter, add up the lengths outlined in red. The perimeter includes the two legs of the triangle and three sides of the square.

Therefore:

Example Question #1142 : Plane Geometry

A right isosceles triangle is stacked on top of a square as shown in the figure. Find the perimeter of the compound shape.

9

Possible Answers:

Correct answer:

Explanation:

 

13

Notice that the hypotenuse of the right isosceles triangle is also the length of a side of the square.

First, we will need to find the length of the legs of the triangle by using the Pythagorean theorem.

Substitute in the given length of the hypotenuse to find the length of the leg of the triangle.

13

In order to find the perimeter, add up the lengths outlined in red. The perimeter includes the two legs of the triangle and three sides of the square.

Therefore:

Example Question #161 : 45/45/90 Right Isosceles Triangles

A right isosceles triangle is stacked on top of a square as shown in the figure. Find the perimeter of the compound shape.

10

Possible Answers:

Correct answer:

Explanation:

13

Notice that the hypotenuse of the right isosceles triangle is also the length of a side of the square.

First, we will need to find the length of the legs of the triangle by using the Pythagorean theorem.

Substitute in the given length of the hypotenuse to find the length of the leg of the triangle.

13

In order to find the perimeter, add up the lengths outlined in red. The perimeter includes the two legs of the triangle and three sides of the square.

Therefore:

Example Question #162 : 45/45/90 Right Isosceles Triangles

A right isosceles triangle is stacked on top of a square as shown in the figure. Find the perimeter of the compound shape.

11

Possible Answers:

Correct answer:

Explanation:

13

Notice that the hypotenuse of the right isosceles triangle is also the length of a side of the square.

First, we will need to find the length of the legs of the triangle by using the Pythagorean theorem.

Substitute in the given length of the hypotenuse to find the length of the leg of the triangle.

13

In order to find the perimeter, add up the lengths outlined in red. The perimeter includes the two legs of the triangle and three sides of the square.

Therefore:

Example Question #161 : 45/45/90 Right Isosceles Triangles

A right isosceles triangle is stacked on top of a square as shown in the figure. Find the perimeter of the compound shape.

12

Possible Answers:

Correct answer:

Explanation:

13

Notice that the hypotenuse of the right isosceles triangle is also the length of a side of the square.

First, we will need to find the length of the legs of the triangle by using the Pythagorean theorem.

Substitute in the given length of the hypotenuse to find the length of the leg of the triangle.

13

In order to find the perimeter, add up the lengths outlined in red. The perimeter includes the two legs of the triangle and three sides of the square.

Therefore:

Example Question #1 : How To Find The Length Of The Side Of A 45/45/90 Right Isosceles Triangle

The perimeter of a 45-45-90 triangle is 100 inches. To the nearest tenth of an inch, what is the length of each leg?

Possible Answers:

Correct answer:

Explanation:

Let  be the length of a leg; then the hypotenuse is , and the perimeter is

Therefore,

Example Question #1141 : Basic Geometry

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Possible Answers:

Correct answer:

Explanation:

Example Question #3 : How To Find The Length Of The Side Of A 45/45/90 Right Isosceles Triangle

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Possible Answers:

Correct answer:

Explanation:

Example Question #1141 : Plane Geometry

Angle  in the triangle shown below is 45 degrees. Side  has a length of 10. What is the length of side ?

Right_triangle_sides_and_points

Possible Answers:

 

Correct answer:

 

Explanation:

Since we know two of the three angles in this triangle, we can calculate the third, .

Therefore this is a 45/45/90 right triangle. Remember that 45/45/90 right triangles are have a leg:leg:hypotenuse ratio of 1:1:.

We know the hypotenuse, , so we can quickly calculate the length of one of the legs, , by dividing by :

To make this look like one of the answer choies, rationalize the denominator by muliplying the fraction by :

 

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